# Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines

arXiv: https://arxiv.org/abs/1712.04144 · HTML: https://mlsanity.com/paper/1712.04144/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2017.

## Built on by (most cited first, 30 of 33)

- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
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- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
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- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Generative modeling with projected entangled-pair states](https://mlsanity.com/paper/2202.08177/) (2022)
- [Tensor networks and efficient descriptions of classical data](https://mlsanity.com/paper/2103.06872/) (2021)
- [Training-efficient density quantum machine learning](https://mlsanity.com/paper/2405.20237/) (2024)
- [Matching Point Sets with Quantum Circuit Learning](https://mlsanity.com/paper/2102.06697/) (2021)
- [Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification](https://mlsanity.com/paper/2101.03154/) (2021)
- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)
- [Quantum Machine Learning for Finance](https://mlsanity.com/paper/2109.04298/) (2021)
- [What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement](https://mlsanity.com/paper/2303.11249/) (2023)
- [F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits](https://mlsanity.com/paper/2110.04253/) (2021)
- [Bayesian Learning of Parameterised Quantum Circuits](https://mlsanity.com/paper/2206.07559/) (2022)
- [Many-body localized hidden generative models](https://mlsanity.com/paper/2207.02346/) (2022)
- [Generative Invertible Quantum Neural Networks](https://mlsanity.com/paper/2302.12906/) (2023)
- [Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity](https://mlsanity.com/paper/2107.00195/) (2021)
- [Deep tensor networks with matrix product operators](https://mlsanity.com/paper/2209.09098/) (2022)
- [Distributive Pre-Training of Generative Modeling Using Matrix-Product States](https://mlsanity.com/paper/2306.14787/) (2023)
- [TabularQGAN: A quantum generative model for tabular data synthesis](https://mlsanity.com/paper/2505.22533/) (2025)
- [Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Function](https://mlsanity.com/paper/2602.22255/) (2026)
- [Application-Oriented Benchmarking of Quantum Generative Learning Using QUARK](https://mlsanity.com/paper/2308.04082/) (2023)
- [Implementing Quantum Generative Adversarial Network (qGAN) and QCBM in Finance](https://mlsanity.com/paper/2308.08448/) (2023)
- [A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data](https://mlsanity.com/paper/2511.13514/) (2025)
- [Sample-efficient Quantum Born Machine through Coding Rate Reduction](https://mlsanity.com/paper/2211.10418/) (2022)
- [Quantum Generative Modeling using Parameterized Quantum Circuits](https://mlsanity.com/paper/2303.16955/) (2023)
- [Quantum Scrambling Born Machine](https://mlsanity.com/paper/2602.17281/) (2026)

## Abstract (arXiv)

We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and quantum states respectively.Classical and quantum information patterns of the target datasets therefore provide principled guidelines for structural design and learning in these two approaches. Taking the restricted Boltzmann machines (RBM) as an example, we analyze the information theoretical bounds of the two approaches. We verify our reasonings by comparing the performance of RBMs of various architectures on the standard MNIST datasets.